Examples of com.opengamma.analytics.financial.model.volatility.local.PureLocalVolatilitySurface

Package com.opengamma.analytics.financial.model.volatility.local

Examples of com.opengamma.analytics.financial.model.volatility.local.PureLocalVolatilitySurface

com.opengamma.analytics.financial.model.volatility.local.PureLocalVolatilitySurface
Under the assumption of cash and proportional discrete dividends, the stock price $S_t$ can be modelled as $S_t = (F_t-D_t)x_t + D_t$ where $F_t$ is the forward, $D_t$ is the growth-rate discounted value of future cash dividends, and $X_t$ is a positive martingale with $X_0 = 1$, known as the pure stock process. If the SDE for the pure stock process is $\frac{dX_t}{X_t} = \sigma^X(t,X_t)dW_t$ then $\sigma^X(t,X_t)$ is the pure local volatility, and can be found by applying the Dupire formula to call options on the the pure stock. See white (2012), Equity Variance Swap with Dividends, for details.

    ArgumentChecker.notNull(swap, "swap");
    ArgumentChecker.notNull(discountCurve, "discount curve");
    ArgumentChecker.notNull(marketVols, "market volatilities");
    final DupireLocalVolatilityCalculator dupire = new DupireLocalVolatilityCalculator();
    final PureImpliedVolatilitySurface pureSurf = getPureImpliedVolFromMarket(spot, discountCurve, dividends, marketVols);
    final PureLocalVolatilitySurface plv = dupire.getLocalVolatility(pureSurf);
    final double t = swap.getTimeToSettlement();
    final double[] ev = VAR_SWAP_BKW_PDE_CALCULATOR.expectedVariance(spot, discountCurve, dividends, t, plv);
    //TODO while calculating both with and without div correction is go for testing, don't want it for production
    final double res = (swap.correctForDividends() ? ev[0] : ev[1]) / t;
    return res;

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    ArgumentChecker.notNull(swap, "swap");
    ArgumentChecker.notNull(discountCurve, "discount curve");
    ArgumentChecker.notNull(dividends, "dividends");
    ArgumentChecker.notNull(marketVols, "market volatilities");


    final PureLocalVolatilitySurface plv = getPureLocalVolFromMarket(spot, discountCurve, dividends, marketVols);
    final EquityDividendsCurvesBundle divCurves = new EquityDividendsCurvesBundle(spot, discountCurve, dividends);
    final LocalVolatilitySurfaceStrike lv = VolatilitySurfaceConverter.convertLocalVolSurface(plv, divCurves);


    final double eps = 1e-5;
    final int index = swap.correctForDividends() ? 0 : 1;
    final double t = swap.getTimeToSettlement();


    //up - here we assume that the local vol surface is invariant to a change of spot and form a new pure local vol surface corresponding to the bumped spot
    final double sUp = spot * (1 + eps);
    final EquityDividendsCurvesBundle divCurvesUp = new EquityDividendsCurvesBundle(sUp, discountCurve, dividends);
    final PureLocalVolatilitySurface plvUp = VolatilitySurfaceConverter.convertLocalVolSurface(lv, divCurvesUp);
    final double up = VAR_SWAP_FWD_PDE_CALCULATOR.expectedVariance(sUp, discountCurve, dividends, t, plvUp)[index];
    //down
    final double sDown = spot * (1 - eps);
    final EquityDividendsCurvesBundle divCurvesDown = new EquityDividendsCurvesBundle(sDown, discountCurve, dividends);
    final PureLocalVolatilitySurface plvDown = VolatilitySurfaceConverter.convertLocalVolSurface(lv, divCurvesDown);
    final double down = VAR_SWAP_FWD_PDE_CALCULATOR.expectedVariance(sDown, discountCurve, dividends, t, plvDown)[index];


    final double delta = (up - down) / 2 / eps / t;
    return delta;
  }

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    ArgumentChecker.notNull(swap, "swap");
    ArgumentChecker.notNull(discountCurve, "discount curve");
    ArgumentChecker.notNull(dividends, "dividends");
    ArgumentChecker.notNull(marketVols, "market volatilities");


    final PureLocalVolatilitySurface plv = getPureLocalVolFromMarket(spot, discountCurve, dividends, marketVols);
    final EquityDividendsCurvesBundle divCurves = new EquityDividendsCurvesBundle(spot, discountCurve, dividends);
    final LocalVolatilitySurfaceStrike lv = VolatilitySurfaceConverter.convertLocalVolSurface(plv, divCurves);


    final double eps = 1e-5;
    final int index = swap.correctForDividends() ? 0 : 1;
    final double t = swap.getTimeToSettlement();


    final double mid = VAR_SWAP_FWD_PDE_CALCULATOR.expectedVariance(spot, discountCurve, dividends, t, plv)[index];
    //up - here we assume that the local vol surface is invariant to a change of spot and form a new pure local vol surface corresponding to the bumped spot
    final double sUp = spot * (1 + eps);
    final EquityDividendsCurvesBundle divCurvesUp = new EquityDividendsCurvesBundle(sUp, discountCurve, dividends);
    final PureLocalVolatilitySurface plvUp = VolatilitySurfaceConverter.convertLocalVolSurface(lv, divCurvesUp);
    final double up = VAR_SWAP_FWD_PDE_CALCULATOR.expectedVariance(sUp, discountCurve, dividends, t, plvUp)[index];
    //down
    final double sDown = spot * (1 - eps);
    final EquityDividendsCurvesBundle divCurvesDown = new EquityDividendsCurvesBundle(sDown, discountCurve, dividends);
    final PureLocalVolatilitySurface plvDown = VolatilitySurfaceConverter.convertLocalVolSurface(lv, divCurvesDown);
    final double down = VAR_SWAP_FWD_PDE_CALCULATOR.expectedVariance(sDown, discountCurve, dividends, t, plvDown)[index];


    final double gamma = (up + down - 2 * mid) / eps / eps / t;
    return gamma;
  }

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    ArgumentChecker.notNull(swap, "swap");
    ArgumentChecker.notNull(discountCurve, "discount curve");
    ArgumentChecker.notNull(dividends, "dividends");
    ArgumentChecker.notNull(marketVols, "market volatilities");


    final PureLocalVolatilitySurface plv = getPureLocalVolFromMarket(spot, discountCurve, dividends, marketVols);
    final EquityDividendsCurvesBundle divCurves = new EquityDividendsCurvesBundle(spot, discountCurve, dividends);
    final LocalVolatilitySurfaceStrike lv = VolatilitySurfaceConverter.convertLocalVolSurface(plv, divCurves);
    final double eps = 1e-5;
    final int index = swap.correctForDividends() ? 0 : 1;
    final double t = swap.getTimeToSettlement();


    //up
    final LocalVolatilitySurfaceStrike lvUp = new LocalVolatilitySurfaceStrike(flooredShiftSurface(lv.getSurface(), eps));
    final PureLocalVolatilitySurface plvUp = VolatilitySurfaceConverter.convertLocalVolSurface(lvUp, divCurves);
    final double up = Math.sqrt(VAR_SWAP_FWD_PDE_CALCULATOR.expectedVariance(spot, discountCurve, dividends, t, plvUp)[index] / t);
    //down
    final LocalVolatilitySurfaceStrike lvDown = new LocalVolatilitySurfaceStrike(flooredShiftSurface(lv.getSurface(), -eps));
    final PureLocalVolatilitySurface plvDown = VolatilitySurfaceConverter.convertLocalVolSurface(lvDown, divCurves);
    final double down = Math.sqrt(VAR_SWAP_FWD_PDE_CALCULATOR.expectedVariance(spot, discountCurve, dividends, t, plvDown)[index] / t);
    final double vega = (up - down) / 2 / eps;
    return vega;
  }

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    ArgumentChecker.notNull(swap, "swap");
    ArgumentChecker.notNull(discountCurve, "discount curve");
    ArgumentChecker.notNull(dividends, "dividends");
    ArgumentChecker.notNull(marketVols, "market volatilities");


    final PureLocalVolatilitySurface plv = getPureLocalVolFromMarket(spot, discountCurve, dividends, marketVols);


    final double eps = 1e-5;
    final int index = swap.correctForDividends() ? 0 : 1;
    final double t = swap.getTimeToSettlement();


    //up
    final PureLocalVolatilitySurface plvUp = new PureLocalVolatilitySurface(flooredShiftSurface(plv.getSurface(), eps));
    final double up = Math.sqrt(VAR_SWAP_FWD_PDE_CALCULATOR.expectedVariance(spot, discountCurve, dividends, t, plvUp)[index] / t);
    //down
    final PureLocalVolatilitySurface plvDown = new PureLocalVolatilitySurface(flooredShiftSurface(plv.getSurface(), -eps));
    final double down = Math.sqrt(VAR_SWAP_FWD_PDE_CALCULATOR.expectedVariance(spot, discountCurve, dividends, t, plvDown)[index] / t);
    final double vega = (up - down) / 2 / eps;
    return vega;
  }

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   * @return The price
   */
  public double priceFromImpliedVolsForwardPDE(final EquityVarianceSwap swap, final double spot, final YieldAndDiscountCurve discountCurve, final AffineDividends dividends,
      final SmileSurfaceDataBundle marketVols) {


    final PureLocalVolatilitySurface pureSurf = getPureLocalVolFromMarket(spot, discountCurve, dividends, marketVols);


    final double[] ev = VAR_SWAP_FWD_PDE_CALCULATOR.expectedVariance(spot, discountCurve, dividends, swap.getTimeToSettlement(), pureSurf);
    final double res = swap.correctForDividends() ? ev[0] : ev[1];
    return res;
  }

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    ArgumentChecker.notNull(swap, "swap");
    ArgumentChecker.notNull(discountCurve, "discount curve");
    final double eps = 1e-5;


    //this surface is assumed invariant to change in the spot
    final PureLocalVolatilitySurface pureSurf = getPureLocalVolFromMarket(spot, discountCurve, dividends, marketVols);


    //price the variance swap by static replication of the log-payoff and dividend correction terms
    final double[] evUp = VAR_SWAP_FWD_PDE_CALCULATOR.expectedVariance((1 + eps) * spot, discountCurve, dividends, swap.getTimeToSettlement(), pureSurf);
    final double[] evDown = VAR_SWAP_FWD_PDE_CALCULATOR.expectedVariance((1 - eps) * spot, discountCurve, dividends, swap.getTimeToSettlement(), pureSurf);

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    ArgumentChecker.notNull(dividends, "dividends");
    ArgumentChecker.notNull(marketVols, "market volatilities");
    final double eps = 1e-5;


    final EquityDividendsCurvesBundle div = new EquityDividendsCurvesBundle(spot, discountCurve, dividends);
    final PureLocalVolatilitySurface pureSurf = getPureLocalVolFromMarket(spot, discountCurve, dividends, marketVols);
    //this surface is assumed invariant to change in the spot
    final LocalVolatilitySurfaceStrike lv = convertLV(pureSurf, div);


    //price the variance swap by static replication of the log-payoff and dividend correction terms
    //up
    final EquityDividendsCurvesBundle divUp = new EquityDividendsCurvesBundle((1 + eps) * spot, discountCurve, dividends);
    final PureLocalVolatilitySurface plvUp = convertLV(lv, divUp);
    final double[] evUp = VAR_SWAP_FWD_PDE_CALCULATOR.expectedVariance((1 + eps) * spot, discountCurve, dividends, swap.getTimeToSettlement(), plvUp);
    //down
    final EquityDividendsCurvesBundle divDown = new EquityDividendsCurvesBundle((1 - eps) * spot, discountCurve, dividends);
    final PureLocalVolatilitySurface plvDown = convertLV(lv, divDown);
    final double[] evDown = VAR_SWAP_FWD_PDE_CALCULATOR.expectedVariance((1 - eps) * spot, discountCurve, dividends, swap.getTimeToSettlement(), plvDown);
    final double res = swap.correctForDividends() ? (evUp[0] - evDown[0]) / spot / eps : (evUp[1] - evDown[1]) / spot / eps;
    return res;
  }

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        final double s = (f - d) * x + d;
        return s / (s - d) * from.getVolatility(t, s);
      }
    };
    return new PureLocalVolatilitySurface(FunctionalDoublesSurface.from(func));
  }

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        final double f = divCurves.getF(t);
        final double s = (f - d) * x + d;
        return volSurface.getVolatility(t, s) * s / (s - d);
      }
    };
    return new PureLocalVolatilitySurface(FunctionalDoublesSurface.from(pureLocalVol));
  }

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com.opengamma.analytics.financial.equity.variance.VarianceSwapWithDividendsTest

com.opengamma.analytics.financial.model.finitedifference.applications.LogPayoffTest

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